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11.
The authors study a discrete-time, infinite-horizon, dynamic programming model for the replacement of components in a binary k-out-of-n failure system. (The system fails when k or more of its n components fail.) Costs are incurred when the system fails and when failed components are replaced. The objective is to minimize the long-run expected average undiscounted cost per period. A companion article develops a branch-and-bound algorithm for computing optimal policies. Extensive computational experiments find it effective for k to be small or near n; however, difficulties are encountered when n ≥ 30 and 10 ≤ k ≤ n − 4. This article presents a simple, intuitive heuristic rule for determining a replacement policy whose memory storage and computation time requirements are O(n − k) and O(n(n − k) + k), respectively. This heuristic is based on a plausible formula for ranking components in order of their usefulness. The authors provide sufficient conditions for it to be optimal and undertake computational experiments that suggest that it handles parallel systems (k = n) effectively and, further, that its effectiveness increases as k moves away from n. In our test problems, the mean relative errors are under 5% when n ≤ 100 and under 2% when k ≤ n − 3 and n ≤ 50. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44, 273–286, 1997. 相似文献
12.
This paper presents a branch and bound algorithm for computing optimal replacement policies in a discrete‐time, infinite‐horizon, dynamic programming model of a binary coherent system with n statistically independent components, and then specializes the algorithm to consecutive k‐out‐of‐n systems. The objective is to minimize the long‐run expected average undiscounted cost per period. (Costs arise when the system fails and when failed components are replaced.) An earlier paper established the optimality of following a critical component policy (CCP), i.e., a policy specified by a critical component set and the rule: Replace a component if and only if it is failed and in the critical component set. Computing an optimal CCP is a optimization problem with n binary variables and a nonlinear objective function. Our branch and bound algorithm for solving this problem has memory storage requirement O(n) for consecutive k‐out‐of‐n systems. Extensive computational experiments on such systems involving over 350,000 test problems with n ranging from 10 to 150 find this algorithm to be effective when n ≤ 40 or k is near n. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 288–302, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10017 相似文献
13.
We consider the problem of assigning a set of jobs to different parallel machines of the same processing speed, where each job is compatible to only a subset of those machines. The machines can be linearly ordered such that a higher‐indexed machine can process all those jobs that a lower‐indexed machine can process. The objective is to minimize the makespan of the schedule. This problem is motivated by industrial applications such as cargo handling by cranes with nonidentical weight capacities, computer processor scheduling with memory constraints, and grades of service provision by parallel servers. We develop an efficient algorithm for this problem with a worst‐case performance ratio of + ε, where ε is a positive constant which may be set arbitrarily close to zero. We also present a polynomial time approximation scheme for this problem, which answers an open question in the literature. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008 相似文献
14.
Most papers in the scheduling field assume that a job can be processed by only one machine at a time. Namely, they use a one‐job‐on‐one‐machine model. In many industry settings, this may not be an adequate model. Motivated by human resource planning, diagnosable microprocessor systems, berth allocation, and manufacturing systems that may require several resources simultaneously to process a job, we study the problem with a one‐job‐on‐multiple‐machine model. In our model, there are several alternatives that can be used to process a job. In each alternative, several machines need to process simultaneously the job assigned. Our purpose is to select an alternative for each job and then to schedule jobs to minimize the completion time of all jobs. In this paper, we provide a pseudopolynomial algorithm to solve optimally the two‐machine problem, and a combination of a fully polynomial scheme and a heuristic to solve the three‐machine problem. We then extend the results to a general m‐machine problem. Our algorithms also provide an effective lower bounding scheme which lays the foundation for solving optimally the general m‐machine problem. Furthermore, our algorithms can also be applied to solve a special case of the three‐machine problem in pseudopolynomial time. Both pseudopolynomial algorithms (for two‐machine and three‐machine problems) are much more efficient than those in the literature. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 57–74, 1999 相似文献
15.
Customer acquisition and customer retention are the most important challenges in the increasingly competitive telecommunications industry. Traditional studies of customer switching always assume that customers are homogeneous, and thus that model customer switching behavior follows a Markov formulation. However, this postulation is obviously inappropriate in most instances. Blumen et al. (Cornell Studies of Industrial and Labor Relations, Cornell University Press, Ithaca, NY, 1955) developed the Mover–Stayer (MS) model, a generalization of the Markov chain model, to relax the requirement of homogeneity and allow the presence of heterogeneity with two different types of individuals—“stayers,” who purchase the same kinds of products or services throughout the entire observation period; and “movers,” who look for variety in products or services over time. There are two purpose of this article. First, we extend the MS model to a Double Mover‐Stayer (DMS) model by assuming the existence of three types of individuals in the market: (1) stable and loyal customers, who have stable usage within the same company; (2) instable but loyal customers, whose usage varies within the same company over time; and (3) disloyal customers, who switch from one company to another to seek for new experiences or/and benefits. We also propose an estimation method for the DMS model. Second, we apply the DMS model to telecommunications data and demonstrate how it can be used for pattern identification, hidden knowledge discovery, and decision making. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012 相似文献
16.
This article studies the inventory competition under yield uncertainty. Two firms with random yield compete for substitutable demand: If one firm suffers a stockout, which can be caused by yield failure, its unsatisfied customers may switch to its competitor. We first study the case in which two competing firms decide order quantities based on the exogenous reliability levels. The results from the traditional inventory competition are generalized to the case with yield uncertainty and we find that quantity and reliability can be complementary instruments in the competition. Furthermore, we allow the firms to endogenously improve their yield reliability before competing in quantity. We show that the reliability game is submodular under some assumptions. The results indicate that the competition in quantity can discourage the reliability improvement. With an extensive numerical study, we also demonstrate the robustness of our analytical results in more general settings. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 107–126, 2015 相似文献
17.
In this article we develop a heuristic procedure for a multiproduct dynamic lot-sizing problem. In this problem a joint setup cost is incurred when at least one product is ordered in a period. In addition to the joint setup cost a separate setup cost for each product ordered is also incurred. The objective is to determine the product lot sizes, over a finite planning horizon, that will minimize the total relevant cost such that the demand in each period for each product is satisfied without backlogging. In this article we present an effective heuristic procedure for this problem. Computational results for the heuristic procedure are also reported. Our computational experience leads us to conclude that the heuristic procedure may be of considerable value as a decision-making aid to production planners in a real-world setting. © 1994 John Wiley & Sons, Inc. 相似文献
18.
This article addresses the inventory placement problem in a serial supply chain facing a stochastic demand for a single planning period. All customer demand is served from stage 1, where the product is stored in its final form. If the demand exceeds the supply at stage 1, then stage 1 is resupplied from stocks held at the upstream stages 2 through N, where the product may be stored in finished form or as raw materials or subassemblies. All stocking decisions are made before the demand occurs. The demand is nonnegative and continuous with a known probability distribution, and the purchasing, holding, shipping, processing, and shortage costs are proportional. There are no fixed costs. All unsatisfied demand is lost. The objective is to select the stock quantities that should be placed different stages so as to maximize the expected profit. Under reasonable cost assumptions, this leads to a convex constrained optimization problem. We characterize the properties of the optimal solution and propose an effective algorithm for its computation. For the case of normal demands, the calculations can be done on a spreadsheet. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:506–517, 2001 相似文献
19.
Lot splitting refers to breaking a production lot into smaller sublots during production. Coordinating lot splitting decisions across multiple stages of a production process is a challenging task. Traditional lot splitting and lot streaming models implicitly assume that the entire system is operated and owned by the same firm, or there exists a coordinator who controls the operation of all machines in the system. In this paper, we consider the situation where the machines in a multiple‐stage production process are owned and managed by different companies. Every item in a given production lot has to go through the processing by the supplier's machine, followed by the manufacturer's machine, and so on. We develop and analyze coordination mechanisms that enable different parties in the supply chain to coordinate their lot splitting decisions so as to achieve a systemwide optimum. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004 相似文献
20.
Logistical planning problems are complicated in practice because planners have to deal with the challenges of demand planning and supply replenishment, while taking into account the issues of (i) inventory perishability and storage charges, (ii) management of backlog and/or lost sales, and (iii) cost saving opportunities due to economies of scale in order replenishment and transportation. It is therefore not surprising that many logistical planning problems are computationally difficult, and finding a good solution to these problems necessitates the development of many ad hoc algorithmic procedures to address various features of the planning problems. In this article, we identify simple conditions and structural properties associated with these logistical planning problems in which the warehouse is managed as a cross‐docking facility. Despite the nonlinear cost structures in the problems, we show that a solution that is within ε‐optimality can be obtained by solving a related piece‐wise linear concave cost multi‐commodity network flow problem. An immediate consequence of this result is that certain classes of logistical planning problems can be approximated by a factor of (1 + ε) in polynomial time. This significantly improves upon the results found in literature for these classes of problems. We also show that the piece‐wise linear concave cost network flow problem can be approximated to within a logarithmic factor via a large scale linear programming relaxation. We use polymatroidal constraints to capture the piece‐wise concavity feature of the cost functions. This gives rise to a unified and generic LP‐based approach for a large class of complicated logistical planning problems. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009 相似文献